Well, think about what goes into firing a torpedo:
1) The torpedo casings are stored in a magazine somewhere close to the launcher. They might or might not have warheads fitted during storage, but if they do have warheads fitted, they aren't "armed" (which in Trek terms means loaded with reactants)
2) The torpedo casings must then be armed. This means that they are put under external power, fueled and armed. They would probably not run under internal power until shortly before actually being launched... make sense?
3) At some point, during or after this, the torpedo casings are moved to a launching queue. They'd be kept under external power during this phase as well. Remember, they now have antimatter inside... so they should be treated with a certain degree of delicacy... don't you think?
4) The queue of armed torpedoes is stored in a "standby firing queue" waiting for deployment. (If they don't get fired, they'd eventually be defueled and disarmed after being pulled from there). Think of this like the "ready-5" status of carrier aircraft more than anything else.
5) The torpedoes in the firing queue then, just before launch, get put onto internal power, moved to a launch tube, and loaded in. They are now ready for immediate firing.
6) The launch tube would reasonably be in a total vacuum and zero gravity, with the torpedos suspended magnetically on the center axis of the launch tube. You don't want or need FRICTION, do you? So there will be a gap between the outside of the torpedo casing and the launch tube. The size of the gap is irrelevant, except in terms of the following.
7) The same magnetic field that is suspending the torpedo on the center axis of the tube then is used, as mentioned before, as a "railgun" to provide a significant initial acceleration of the torpedo beyond the ship without requiring the torpedo to use its own fuel supplies to do so.

At a safe distance from the ship's hull, the torpedo's engine cuts in and further accelerates the weapon. It can either go into a straight linear acceleration (gaining much higher velocity at the expense of maneuverability) or it can accelerate more slowly, reserving fuel for maneuverability. This would be decided by the weapons control officer prior to weapon launch. Think of it as "homing mode" versus "ballistic mode." (You might also have "mine mode?")
9) The device would track to the target, and would detonate its payload under certain preprogrammed conditions. This would include "self-destruct," "proximity charge" and "impact detonation" modes, I think. I can't come up with any other modes you'd really need... maybe a "delay after impact" mode to allow ballistic penetration before detonation, but with the yields we're talking here and the speeds we're talking here I can't see that as being necessary or practical.
Anyway... attack. Pick all that apart to whatever extent you like. But it has the following effects:
1) It explains the slow loading (the arm isn't just a crane arm, it's also the external power feed and the matter/antimatter loader).
2) It explains the disproportionality of the launch tube, and the variety of casing shapes and sizes which can be launched.
Oh, and it explains a lot of other things as well, but much of that is subject to debate (for instance, you could argue that in TOS the torpedos were launching from the dorsal, but only igniting their engines a significant distance ahead... so it LOOKED like they were coming from the p-hull from the angle we saw them!)
Attack!
